Yes, of course. Chihuahuas, of course, among many others. And there were some paintings and some figures--the example Wikipedia links to looks very un-stylized and doggy. There was nothing about how frequently dogs were portrayed, but since they ate dogs they may not have thought them as quite as suitable for dramatic art as jaguars.
But one link leads to another(*)--did Indians domesticate coyotes? There aren't any Hare Indian's left, but maybe there are bones somewhere. The argument went that they looked like them (but other dogs do too), sounded like them (other dogs don't), other dogs hated them (as though they were another species). Not overwhelming arguments, but if people can find a little DNA somewhere, it might be worth checking. If wolves, and foxes, and culpeos, why not coyotes?
(*) Which leads to not getting any writing done...
UPDATE : See Retriever's detailed comment.